First, I'm going to get this out of the way: I know next to nothing about music theory, and couldn't compose a technical song for crap. I understand the ideas behind timing, but can't put them to use myself. The way I write and learn pieces of music is by listening and "feeling" the rhythm.

Here's my problem: I can only seem to "feel" the rhythms for 2/4, 4/4, and 6/8 time. Can anyone please give me a suggestion to try and expand my ability to play in different time signatures?

And sorry if the bit about me feeling the timing is weird or obscure. I just seem to naturally pick those three times up with little to no trouble. Anything else is well beyond me.
My heart beats in 4/4, not the other way around.

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In many cultures the timing is internal and part of the music. The Afro Cuban Clave Rhythm for example consists of two alternating measures one "3" and the second "2" or reverversed 2 3.

So, there are two asymmetric measures, which fit within a 4/4/ western time signature yet within the 2 measure Clave, it is a completely different way than external (metronome) time we normally use.

This may sound totally retarded but the ballroom dancing sites for Salsa, Merenge, Samba, Mambo, and other Latin Jazz styles tend to have useful exercises to practice. It takes some time to get the feel of Clave - as the timing does not correspond to our western system of quarter notes, triplets, etc. It is a separate and independent time keeping system. But it works with 4/4 time just fine.

If I find the links that I used I'll post them. There's also a DVD "Conversations in Clave" you might want to check out.

At the very base is a 3 measure followed by a two measure. And listen to it over and over and eventually you get the feel of it. You will know when it happens zI think.
To become able to feel these signatures you have to get used to them. I did the following: get a drum computer/program and compose a very simple beat in whatver odd signature you want to practice, start off with 5/4 an 7/8. Put the beat on loop and start jamming. This is a total pain in the ass the first few times you do it, because the rythmn will not be natural to you. But hey, practice makes perfect, the longer you jam to them the more you will be able to do within these time signatures.

Try starting with playing a 7 note lick on in a7/8 signature. Once you get it down, and you start to feel the lick. Try switching notes, leave some out, start on on the 2nd 8th note and play a 6 note lick. All these kind of practices will make you become more familiar with odd time signatures.

I Hope this helps, its how I did/do it.
Wow, thanks. I didn't really understand much about the Afro Cuban Clave thing you were talking about, but the idea to look on some dancing sites sounds interesting. I'll have to try it out.

The idea for the drum machine sounds really helpful too. Would a metronome be a good substitute for a drum machine?
My heart beats in 4/4, not the other way around.

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I like to think of all timings starting from 2 or 3 beats a measure. Every other time signature is just a combination of that.

For example 7/4 You could count, 1-2 1-2 1-2-3 or if you want to combine the 1-2's, 1-2-3-4 1-2-3.

Don't let this mislead you to think the 1's are the accentuated beats. That is left to be determined by the song itself.

Sorry if that didn't help